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Question

1-If , find the average rate of change on the interval [−1, 2].

2-If f (t) = t² + t, find [ f(t + h) – f (t)] / h.

3-If f(x) = 2x + 1, what is the domain?

4-Find the range of f (x) = – 1 / √ (2 – x)

5-Find the range of 

Answer 1

f(2)= 6, f(-1)=0 ... delta f = 6-0=6 ... delta t = 2-(-1)=3 ... avg rate of change = delta f/delta t = 6/3 = 2

(f(t+h)-f(t))/h = (t^2+2th+h^2+t+h-t^2-t)/h = (2th+h^2+h)/h= 2t+h+1

f(x) = 2x+1 ... f is valid for all x ... domain is all real x

f(x) = -1/sqrt(2-x) ... range = +/- infinity

f(x)=2-sqrt(2-x) ... range = +/- infinity